Permutations & Combinations

Count arrangements and selections with nPr, nCr and factorials, showing when order matters. Try “how many ways to choose 3 from 10?”.

Try an example:

How the Permutations & Combinations works

  1. Decide whether order matters: yes for permutations, no for combinations.
  2. Use nPr = n! ÷ (n − r)! or nCr = n! ÷ (r!(n − r)!).
  3. Cancel the factorials and calculate (10C3 = 120).

Frequently asked questions

What is the difference between a permutation and a combination?

A permutation counts ordered arrangements; a combination counts unordered selections.

What is 0!?

By definition, 0! = 1.

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